Cryptology ePrint Archive: Report 2006/345

Private and Efficient Stable Marriages (Matching)

Atkinson, T. and Bartak,R. and Silaghi,M.-C. and Tuleu,E. and Zanker,M.

Abstract: We provide algorithms guaranteeing high levels of privacy by computing
uniformly random solutions to stable marriages problems. We also
provide efficient algorithms extracting a non-uniformly random
solution and guaranteeing t-privacy for any threshold t. The most
private solution is expensive and is based on a distributed/shared CSP model of the problem. The most efficient version is based on running the Gale-Shapley algorithm after shuffling the men (or women) in the
shared secret description of the problem.

We introduce an efficient arithmetic circuit for the Gale-Shapley
algorithm that can employ a cryptographic primitive
we propose for vector access with an arbitrary number of participants.

Participants want to find a stable matching
as defined by their secret preferences and without leaking any of these secrets.

An additional advantage of the solvers based on secure simulations of
arithmetic circuits is that it returns a solution picked randomly
among existing solutions. Besides the fact that this increases privacy
to a level of requested t-privacy, it also provides fairness
to participants.
A real implementation of a described secure solution usable by
participants on distinct computers on the Internet is implemented (by students in a class assignment) and is available on our web-site.

Category / Keywords:

Publication Info: Full version of the ECAI 2006 Workshop on DCSP, Italy, August 2006